4th grade: week 7 ~ activity set 1€¦ · 4th grade: week 6 ~ activity set 2 hi, 4th graders!...

$: 4th Grade: Week 7 ~ Activity Set 1€¦ · 4th Grade: Week 6 ~ Activity Set 2 Hi, 4th graders! Today, you will c reate area models to represent and solve a whole number times a fraction$
4th Grade: Week 7 ~ Activity Set 1

Hello 4th graders! Welcome to another fun filled week of math! For the next few weeks, we will be multiplying fractions by whole numbers. Since we have worked so much with fractions this year, let’s see how much you remember before we take the next step! As you recall, we can write the fraction 6/8 as the sum of unit fractions. (Remember that unit fractions have a numerator of 1).

There is of a pizza in the pizza box.86

How can I think of ?8

6

As a Visual Model

81 8

1 81 8

1 81 8

1

As a Repeated Addition Equation

+ + + + + =81

81

81

81

81

81

86

In my model and addition equation, I see

6 groups of .81

That makes me think of multiplication!

As a Multiplication Equation

= 6 x 86

81

(6 groups of )81

Write a multiplication equation for each repeated addition sentence. Then solve.

Addition Sentence Multiplication Equation

+ + + = n51

51

51

51 n =

+ + = m91

91

91 m =

+ + + + + + = a41

41

41

41

41

41

41 a =

Complete the table. The first one has been done for you.

Fraction Repeated Addition Sentence Multiplication Sentence

Example 83 + +8

181

81 3 x 8

1 1.

54 4 x 5

1 2. +9

191 2 x 9

1 3.

43

4. + + +61

61

61

61

Let’s see if we can apply our learning in a story problem. Natalie baked a pan of brownies and cut it into 10 equal pieces.

She gave one brownie to each of her 6 best friends. Write the amount of brownies given as both an addition equation (using unit fractions) and a multiplication equation. (Remember that an equation has an answer).

Addition Equation Multiplication Equation

Just one more thing: What addition equation and related multiplication is represented by this number line?

Addition Equation Multiplication Equation

4th Grade: Week 6 ~ Activity Set 2 Hi, 4th graders! Today, you will create area models to represent and solve a whole number times a fraction multiplication problems.

Think back a whole year ago to when you were a 3rd grader. You started learning about multiplication of whole numbers like 3 x 4.

I remember 3 x 4 means 3 groups of 4.

Picture of Equal Groups

Repeated Addition

Array

4 + 4 + 4

You can use the same thinking when multiplying a whole number times a fraction.

Jeff practiced playing drums for of an hour 4 times today! (He is very dedicated).32

What is the total amount of time that Jeff practiced?

You can show this with an area model.

32

32

32

32

...and a repeated addition equation

+ + + = 3

232

32

32

38

Jeff practiced , or38

2 hours today.,32

...and a multiplication equation

4 x = 3

238

4 groups of equals 32

38

YOUR TURN! Shade in each area model to represent the story. Highlight the cells and click the fill bucket above. Then, write a repeated addition equation and multiplication equation to match your area model.

Story Area Model Repeated Addition Equation Gina made 3 batches

of brownies. Each batch has of a cup4

3 of cocoa.

How much cocoa did

Gina use for all 3 batches?

Batch 1 Batch 2 Batch 3

Multiplication Equation


Story Area Model Repeated Addition Equation Matt and Tony each

ate of a pizza.65

How much did they eat

combined?

Matt’s Pizza Tony’s Pizza Multiplication Equation

For the next two problems, draw your own area models. You may insert a picture or just describe how you drew them at home.

Story Area Model Repeated Addition Equation Olivia ran of a mile5

4 each day for 3 days.

What is the total

distance Olivia ran?


Story Area Model Repeated Addition Equation Taylor bought 6

packages of jelly beans. Each package weighs of a pound.2

1

What is the total weight of the packages?

Hmm...how many

ounces would that be?


Did you notice how I snuck a measurement conversion problem in there. Pretty clever. 😉 Now, we will wrap up with a multiplicative comparison problem!

Laura’s hedgehog, Waldo weighs of a pound. Her kitten, Beckham,43

weighs 4 times as much as Waldo. How much does Beckham weigh?


Yesterday, you created area models to represent and find the product of a whole number and a fraction. Today, you will… yes, you guessed it… build number lines to show this thinking! Quick Review

A fraction number line shows how whole numbers are

partitioned in equal parts.

This fraction number line is partitioned into fourths.

Complete these equivalencies

about the number line.

= ___44

2 = We can use this same number line to multiply a whole number and a fraction.

Jared bought 3 boxes of nails.

Each box weighs of a43

pound.

How much do the boxes weigh together?

Think…

I know I have 3 groups (boxes).

Each group holds lb.43

On my number line, I can skip count or jump every .43

+ + = ___ lbs.43

43

43

____ x = ___ lbs.43

groups of

Answer the questions and write equations about the story and number line.

Each of Lola’s 7 guinea pigs is

of a foot long.21

If Lola lines them up, how long

is the row of guinea pigs?

How many groups? _______

How much in each group? ____

How many jumps? _______ What is each jump worth? _______

Repeated Addition Equation


Create your own number line to represent each story. Be sure to partition precisely and label your work. You may insert a picture or just describe how you drew it at home.

Adam roller skates of a mile32

each loop around the path.

How far does Adam skate 4 times around the path?



Number Line



Nicole cut a board into 2 equal

pieces. Each piece is of a65

yard long.

How long was the board before Nicole cut it?



Number Line



Now, see if you can create a number line based on only the multiplication equation.

4 x = _____83

Number Line

3 x = _____52

Number Line

Thank you for working so hard to partition precisely and skip jump carefully! If the weather is nice, maybe you can spend some time outside skipping or jumping. If it is rainy, maybe just jump over the puddles. 😊


WOW! You have been working hard this week on building an understanding of multiplying with fractions! In the next few activity sets, you will learn how to multiply a whole number and a mixed number in order to solve real-world problems involving fractions. First, let’s review the different ways that we can represent mixed numbers:

Mixed Number

Area Model Number Line Improper Fraction

2 43

We read this as:

Two and three-fourths

2 is located between4

3 2 and 3 on the number line.

I can express 2 as the sum of two fractions, then add three-fourths, to find the improper fraction.

Complete the chart by writing or drawing the missing representations.

Mixed Number

Area Model

Improper Fraction (Show the fraction addition

equation.)

It is between which 2 whole

numbers?

3 31 1.)

+ + + = 33

33

33

31

310

3 and 4

2.)

3.)

4.)

5.) 6.)

+ + = 88

88

83

819

7.)

4th Grade: Week 7 ~ Activity Set 4 Now, we will review adding mixed numbers, so that we can apply that skill to understanding multiplying with a mixed number.

Problem Area Model Repeated Addition Strategy

Ginger is making 3 scarves for her friends.

She needs 1 yards of32

fabric for each scarf.

How many total yards of fabric does Ginger

need for the 3 scarves?

1 + 1 +1 = n32

32

32

1) Add the whole numbers, then add the fractions.

1 + 1 + 1 = 3

+ + = or 232

32

32

36

2) Combine the whole number and the sum of the fractions to find the total yards.

So, 3 + 2 = 5.

Ginger needs 5 yards of fabric.

It’s your turn to use the repeated addition strategy to solve some problems!

1.)Kyle needs four wooden boards to build a border around his garden. The length of each side measures 3 ft.6

1 How many total feet of wood does Kyle need?

Area Model:

Repeated Addition Strategy:

2.)Jen uses 2 cups of apples in each41

homemade pie. She makes 3 pies. How many cups of apples does Jen need to make the pies?

Area Model:


3.)Charlie walks 1 miles each day87

for 5 days. How many total miles does Charlie walk?

Area Model:


4th Grade: Week 7 ~ Activity Set 4 Earlier this week, we made a connection between writing a repeated addition equation and using multiplication, in order to multiply a whole number and a fraction. Let’s take a look at that connection when we multiply a whole number and a mixed number.

Problem Repeated Addition Multiplication

Sarah plays soccer for 3 43

hours at each practice two days per week.

How many hours total does Sarah play soccer each week?

3 + 3 = n43

43

Step 1: 3 + 3 = 6

+ = or 143

43

46

42

Step 2: 6 + 1 = 7 hours4

242

Decompose the mixed number into a whole number and a fraction.

2 x 3 = n43

2 x 3 = 6 2 x = or 14

346

42

6 + 1 = 7 hours42

42

What do you notice about these

two different strategies?

Solve the following problems by decomposing the mixed number and multiplying. Show your work!

1.) 2 x 4 =82 2.) 5 x 2 =4

3 3.) Julie’s new kitten weighs 3 pounds. Her older cat weighs four times as much as the new kitten.6

4 How much does Julie’s older cat weigh?

_________ pounds 4.) Max needs 28 inches of brick to finish his new sidewalk. He buys 5 bricks that each measure 5 2

1

inches in length. Part A: What is the length of all the bricks that Max buys, if they are placed end-to-end?

_________ inches Part B: Did Max buy enough bricks to finish his sidewalk? YES or NO Show your thinking.

4th Grade: Week 7 ~ Answer Key

Activity Set 1 Page 1 Page 2

Multiplication Equations #1 + + + 51

51

51

51

4 x 51 n= 5

4 #2 92

3 x 91 m= 9

3 #3 + + and 3 x 41

41

41

41

7 x 41 a= or 2 4

741 #4 and 4 x 6

461

Page 2 Addition Equation Multiplication Equation

Brownie Problem + + + + + = 110

110

110

110

110

110

610 6 x = 1

10610

Number Line + + + + = 61

61

61

61

61

65 5 x = 6

165

Activity Set 2

Area Model Repeated Addition Multiplication Equation

Page 1

Cups of Flour

+ + = or 2 cups43

43

43

49

41 3 x = or 2 cups4

349

41

Page 2

Pizza

+ = or 1 pizzas65

65

610

64

2 x = or 16

56

1064

pizzas

Running Distance

+ + = or 254

54

54

512

52

miles

3 x = or 2 miles54

512

52

Pounds of Jelly Beans

+ + + + + =21

21

21

21

21

21

26

or 3 lbs. 6 x = or 3 lbs.2

126

3 x16 = 48 oz. of jelly beans

Weight of Beckham

+ + + = or 3 lbs.43

43

43

43

412 4 x = or 3 lbs.4

34

12

Activity Set 3 - Page 1

Page 1 Number Line

= 144 2 = 4

8

Pounds of Nails + + = lbs.43

43

43

49 3 x = lbs. or 2 lbs.4

349

41

Guinea Pig Length

7 groups (jumps) foot in each group or jump2

1

+ + + + + + =21

21

21

21

21

21

21

27 7 x = ft. or 3 ft.2

127

21

Page 2 Roller Skates

4 groups mile in each3

2 loop

+ + + = or 232

32

32

32

38

32

miles

4 x = or 2 miles32

38

32

Board

2 groups yard in piece6

5

+ = yards or 1 yards65

65

610

64

2 x = yards or 1 yards65

610

64

4 x = or 18

38

12

84

3 x = or 15

256

51


#1 #2 #3 #4 #5 #6 #7

1 6

5

+ = 66 5

6 611

1 and 2

2 8

3

2 and 3


#1

3 + 3+ 3 + 3 = 12 + + + = 61

61

61

61

64

12 + = 12 feet64

64

#2

2 + 2 + 2 = 6 + + = 41

41

41

43

6 + = 6 cups43

43

#3

1+ 1 + 1 + 1 + 1 = 5

+ + + + = = 487

87

87

87

87

835

83

5 + 4 = 9 miles83

83


#1 2 x 4 = 882

84 2 x 4 = 8 2 x = 8 + = 88

284

84

84

#2 5 x 2 = 1243

43 5 x 2 = 10 5 x = = 2 10 + 2 = 124

34

1543

43

43

#3 4 x 3 = 14 pounds64

64 4 x 3 = 12 4 x = = 2 12 + 2 = 146

46

1664

64

64

#4 Part A: 5 x 5 = 27 inches2

121

Part B: No. Since 27 inches is less than 28 inches, Max does not have2

1 enough bricks to finish his new sidewalk.

4th grade: week 7 ~ activity set 1€¦ · 4th grade: week 6 ~ activity set 2 hi, 4th graders!...

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